TopoBio: Data-driven Topology of Biological Soft Matter

Active matter systems are characterized by continuous injection or conversion of energy into the system from its constituents; examples of such systems include flocks of bird, colonies of bacteria, and synthetic microswimmers. As active matter is not in thermodynamic equilibrium, such systems inevitably exhibit complex structure and dynamics, often in the form of concerted motion and complex phase transitions. The structures and transitions and a number of open questions surrounding these are the central objects of study in this project.

I propose to use methods from topological data analysis (TDA) that have been successful in improving our understanding of an array of systems in fields from social sciences and finance to theoretical physics and chemistry. TDA is particularly promising in the context of active matter due to the methods' ability to resolve and quantifying structure in complex data, which is exactly what is needed to address the challenges in active matter.